Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

An Introduction to Magnetohydrodynamics

We develop and test a method for measuring the gravitational lensing induced distortion of faint background galaxies. We first describe how we locate the galaxies and measure a 2-component `polarisation' or ellipticity statistic $e_\alpha$ whose expectation value should be proportional to the gravitational shear $\gamma_\alpha$. We then show that an anisotropic instrumental psf perturbs the polarisation by $\delta e_\alpha = P^s_{\alpha\beta} p_\beta$, where $p_\alpha$ is a measure of the psf anisotropy and $P^s_{\alpha\beta}$ is the `linearised smear polarisability tensor'. By estimating $P^s_{\alpha\beta}$ for each object we can determine $p_\alpha$ from the foreground stars and apply a correction $-P^s_{\alpha\beta}p_\beta$ to the galaxies. We test this procedure using deep high-resolution images from HST which are smeared with an anisotropic psf and then have noise added to simulate ground-based observations. We find that the procedure works very well. A similar analysis yields a linear shear polarisability tensor $P^\gamma_{\alpha\beta}$ which describes the response to a gravitational shear. This calibrates the polarisation-shear relation, but only for galaxies which are well resolved. To empirically calibrate the effect of seeing on the smaller galaxies we artificially stretch HST images to simulate lensing and then degrade them as before. These experiments provide a rigorous and exacting test of the method under realistic conditions. They show that it is possible to remove the effect of instrumental psf anisotropy, and that the method provides an efficient and quantitative measurement of the gravitational shear.

A Method for Weak Lensing Observations

Now more than ever, Gravitation and Spacetime, Second Edition, by Hans C. Ohanian and new coauthor Remo Ruffini, deserves John Wheeler's praise as "the best book on the market today of 500 pages or less on gravitation and general relativity." Gravitation and Spacetime has been thoroughly updated with the most exciting finds and hottest theoretical topics in general relativity and cosmology. Highlights of the revision include the rise and fall of the fifth force, principles and applications of gravitational lensing, COBE's spectacular confirmation of the blackbody spectrum of the cosmic thermal radiation, theories of dark matter and inflation, and the early universe as a testing ground for particle physicists' unification theories, and much, much more. The ideal choice for a graduate-level introduction to general relativity, Gravitation and Spacetime is also suitable for an advanced undergaduate course.

Gravitation and spacetime.

We have analyzed archival HST F606W images of 18 dwarf elliptical (dE) galaxy candidates in the Coma Cluster. We model the full radial extent of their light-profiles by simultaneously fitting a PSF-convolved Sersic R^(1/n) model and, when necessary, either a central point-source or a central PSF-convolved Gaussian. The luminosities of the central component L_nuc scale with the host galaxy luminosity L_gal such that L_nuc = 10^(4.76 +/- 0.10)*(L_gal/10^7)^(0.87 +/- 0.26). The underlying host galaxies display systematic departures from an exponential model that are correlated with the model-independent host galaxy luminosity and are not due to biasing from the nuclear component. The Pearson correlation coefficient between log(n) and central galaxy surface brightness mu_0 (excluding the flux from extraneous central components) is -0.83 at a significance level of 99.99%. The Pearson correlation coefficient between the logarithm of the Sersic index `n' and the host galaxy magnitude is -0.77 at a significance of 99.9%. We explain the observed relationship between dE galaxy luminosity and inner logarithmic profile slope (gamma-prime) as a by-product of the correlation between luminosity and Sersic index n. Including, from the literature, an additional 232 dE and E galaxies spanning 10 mag in absolute magnitude (M), the dE galaxies are shown to display a continuous sequence with the brighter E galaxies such that mu_0 brightens linearly with M until core formation causes the most luminous (M_B _e) diagram, and the _e-log(R_e) diagram have nothing to do with core formation, and are in fact expected from the continuous and linear relation between M and mu_0 and M and log(n).

HST photometry of dwarf elliptical galaxies in Coma, and an explanation for the alleged structural dichotomy between dwarf and bright elliptical galaxies

Recent high-resolution N -body CDM simulations indicate that nonsingular three-parameter models such as the Einasto profile perform better than the singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a wide range of dark matter haloes. While many of the basic properties of the Einasto profile have been discussed in previous studies, a number of analytical properties are still not investigated. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halo, is still lacking to date. To this aim, we used a Mellin integral transform formalism to derive a closed expression for the Einasto surface density and related properties in terms of the Fox H and Meijer G functions, which can be written as series expansions. This enables arbitrary-precision calculations of the surface density and the lensing properties of realistic dark matter halo models. Furthermore, we compared the Sersic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.

https://www.aanda.org/articles/aa/pdf/2012/04/aa18543-11.pdf

Analytical properties of Einasto dark matter haloes

Recent high-resolution N-body CDM simulations indicate that nonsingular three-parameter models such as the Einasto profile perform better than the singular two-parameter models, e.g. the Navarro, Frenk and White, in fitting a wide range of dark matter haloes. While many of the basic properties of the Einasto profile have been discussed in previous studies, a number of analytical properties are still not investigated. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halo, is still lacking to date. To this aim, we used a Mellin integral transform formalism to derive a closed expression for the Einasto surface density and related properties in terms of the Fox H and Meijer G functions, which can be written as series expansions. This enables arbitrary-precision calculations of the surface density and the lensing properties of realistic dark matter halo models. Furthermore, we compared the Sersic and Einasto surface mass densities and found differences between them, which implies that the lensing properties for both profiles differ.

/pdf/analytical-properties-of-einasto-dark-matter-haloes-otckuocnk4.pdf

Ion composition of substorms during storm-time and non-storm-time periods

We present a simple model for the non-thermal emission from the historical supernova remnant SN 1006. We constrain the synchrotron parameters of the model with archival radio and hard X-ray data. Our stationary emission model includes two populations of electrons, which is justified by multi-frequency images of the object. From the set of parameters that predict the correct synchrotron flux we select those which are able to account, either partly or entirely, for the gamma-ray emission of the source as seen by HESS. We use the results from this model as well as the latest constraints imposed by the Fermi observatory and conclude that the TeV emission cannot be accounted for by neutral pion decay produced by high-energy cosmic rays with a single "soft" power-law distribution (i.e., with a particle index greater than 2 or so).

On the Nature of the TeV Emission from the SNR SN 1006

We investigate the properties of static and axisymmetric vacuum solutions of Einstein equations which generalize the Schwarzschild spherically symmetric solution to include a quadrupole parameter. We test all the solutions with respect to elementary and asymptotic flatness and curvature regularity. Analysing their multipole structure, according to the relativistic invariant Geroch definition, we show that all of them are equivalent up to the level of the quadrupole. We conclude that the q -metric, a variant of the Zipoy–Voorhees metric, is the simplest generalization of the Schwarzschild metric, containing a quadrupole parameter.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsos.170826

Francisco Frutos-Alfaro

Papers

Analytical properties of Einasto dark matter haloes

Analytical properties of Einasto dark matter haloes

Ion composition of substorms during storm-time and non-storm-time periods

On the Nature of the TeV Emission from the SNR SN 1006

Comparison of vacuum static quadrupolar metrics.